The Central Argument
How does Newton establish the Law of Universal Gravitation?
What assumptions does it rest on?
- Definitions
o Quantity of Matter Defined
o Quantity of Motion Defined
o Inherent Force (Inertia, vis insita) Defined
o Impressed Force (vis impressa) Defined
o Centripetal Force Defined
o Absolute Quantity of Centripetal Force Defined
o Accelerative Quantity of Centripetal Force Defined
o Motive Quantity of Centripetal Force Defined
- Axioms, or Laws of Motion
o 1. Every body continues in its state of resting or of moving uniformly in a straight line, except insofar as it is driven by impressed forces to alter its state.
o 2. The change of motion is proportional to the motive force impressed, and takes place following the straight line in which that force is impressed.
o 3. To an action there is always a contrary and equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts.
- Rules of Philosophizing
o 1. That there ought not to be admitted any more causes of natural things than those which are both true and sufficient to explain their phenomena.
o 2. Accordingly, to natural effects of the same kind the same causes should be assigned, as far as possible.
o 3. The qualities of bodies that do not suffer intensification and remission, and that pertain to all bodies upon which experiments can be carried out, are to be taken as qualities of bodies universally.
o 4. In experimental philosophy, propositions gathered from the phenomena by induction are to be takes as true, whether exactly or approximately, contrary hypotheses notwithstanding, until other phenomena appear through which they are either rendered more accurate or liable to exceptions.
What evidence does he use?
- Newton used minimal experimental data. His main experimental foundations, the “Phenomena” of Book III, were very far from being pure observations, but they were based on observations and theory generally accepted. Everything was deduced, using mathematical demonstrations, from these few observation-based conclusions about how our world works.
“Preface of the reader” by Newton:
“And on that account we present these (writings) of ours as the mathematical principles of philosophy. For the whole difficulty of philosophy appears to turn upon this: that from the phenomena of motion we investigate the forces of nature, and then from these forces we demonstrate the rest of the phenomena. … In the third book,…, we present an example of this procedure, in the unfolding of the system of the world. For there, from the celestial phenomena, using the propositions demonstrated mathematically in the preceding books, we derive the forces of gravity by which bodies tend to the sun and the individual planets. Then from the forces, using propositions that are also mathematical, we deduce the motions of the planets, of comets, of the moon, and of the sea. In just the same way it would be possible to derive the rest of the phenomena of nature from mechanical principles by the same manner of argument.”
Newton was better than Kepler in two ways.
1. His theory was universal (terrestrial heaviness and the forces that move the planets were a single phenomenon)
2. Newton’s system required fewer contrivances and ad hoc assumptions than Kepler’s.
What are the main steps in the argument and how do we know they are true?
The core sequence is as follows:
1. The mathematical foundations for the development of universal gravitation and celestial mechanics are found in the Definitions, Laws of Motion, and some basic hypothetical mathematical propositions (first 17 prop. Of book 1)
2. Book III, Phenomena. A small number of conclusions about our world.
3. Book III (first 13 prop.), propositions of the application to our universe. Here lies the derivation of universal gravitation: the discovery that the moon is falling just like a rock (or pendulum bob), that inertial and gravitational mass are quantitatively the same, that every particle attracts every other particle inversely as the square of their distance.
4. Having established these things, we can use them to prove that the planets will move in ellipses.
Newton’s main argument is the establishment of universal gravitation and its use to demonstrate the elliptical orbits of the planets.
What questions remain, if any?
- What is the final cause and what is the relation of God with Newton’s theory.
- “He (God) governs everything, not as the soul of the world, but as the lord of all things.”
- “He is eternal and infinite, omnipotent and omniscient; that is, he endures from eternity to eternity, and is present from infinity to infinity. He reigns over everything, and knows everything that happens or can happen.”
- “God is one and the same God always and everywhere. He is omnipresent not in power alone, but also in substance. For power cannot subsist without substance. In him all things are contained and moved, but without mutual effects. God is not affected by the motions of bodies, and these do not experience any resistance from God’s omnipresence. It is universally acknowledged that the highest God exists necessarily, and by the same necessity he is always and everywhere.”
- “Hitherto I have set forth the phenomena of the heavens and of our sea through the force of gravity, but I have not yet assigned the cause of gravity.”
Remember: The Law of Universal Gravitation is not just that all particles with mass gravitate towards each other, but that they do so proportionately to the mass of each body and inversely as the square of the distances between the bodies.
What assumptions does it rest on?
- Definitions
o Quantity of Matter Defined
o Quantity of Motion Defined
o Inherent Force (Inertia, vis insita) Defined
o Impressed Force (vis impressa) Defined
o Centripetal Force Defined
o Absolute Quantity of Centripetal Force Defined
o Accelerative Quantity of Centripetal Force Defined
o Motive Quantity of Centripetal Force Defined
- Axioms, or Laws of Motion
o 1. Every body continues in its state of resting or of moving uniformly in a straight line, except insofar as it is driven by impressed forces to alter its state.
o 2. The change of motion is proportional to the motive force impressed, and takes place following the straight line in which that force is impressed.
o 3. To an action there is always a contrary and equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts.
- Rules of Philosophizing
o 1. That there ought not to be admitted any more causes of natural things than those which are both true and sufficient to explain their phenomena.
o 2. Accordingly, to natural effects of the same kind the same causes should be assigned, as far as possible.
o 3. The qualities of bodies that do not suffer intensification and remission, and that pertain to all bodies upon which experiments can be carried out, are to be taken as qualities of bodies universally.
o 4. In experimental philosophy, propositions gathered from the phenomena by induction are to be takes as true, whether exactly or approximately, contrary hypotheses notwithstanding, until other phenomena appear through which they are either rendered more accurate or liable to exceptions.
What evidence does he use?
- Newton used minimal experimental data. His main experimental foundations, the “Phenomena” of Book III, were very far from being pure observations, but they were based on observations and theory generally accepted. Everything was deduced, using mathematical demonstrations, from these few observation-based conclusions about how our world works.
“Preface of the reader” by Newton:
“And on that account we present these (writings) of ours as the mathematical principles of philosophy. For the whole difficulty of philosophy appears to turn upon this: that from the phenomena of motion we investigate the forces of nature, and then from these forces we demonstrate the rest of the phenomena. … In the third book,…, we present an example of this procedure, in the unfolding of the system of the world. For there, from the celestial phenomena, using the propositions demonstrated mathematically in the preceding books, we derive the forces of gravity by which bodies tend to the sun and the individual planets. Then from the forces, using propositions that are also mathematical, we deduce the motions of the planets, of comets, of the moon, and of the sea. In just the same way it would be possible to derive the rest of the phenomena of nature from mechanical principles by the same manner of argument.”
Newton was better than Kepler in two ways.
1. His theory was universal (terrestrial heaviness and the forces that move the planets were a single phenomenon)
2. Newton’s system required fewer contrivances and ad hoc assumptions than Kepler’s.
What are the main steps in the argument and how do we know they are true?
The core sequence is as follows:
1. The mathematical foundations for the development of universal gravitation and celestial mechanics are found in the Definitions, Laws of Motion, and some basic hypothetical mathematical propositions (first 17 prop. Of book 1)
2. Book III, Phenomena. A small number of conclusions about our world.
3. Book III (first 13 prop.), propositions of the application to our universe. Here lies the derivation of universal gravitation: the discovery that the moon is falling just like a rock (or pendulum bob), that inertial and gravitational mass are quantitatively the same, that every particle attracts every other particle inversely as the square of their distance.
4. Having established these things, we can use them to prove that the planets will move in ellipses.
Newton’s main argument is the establishment of universal gravitation and its use to demonstrate the elliptical orbits of the planets.
What questions remain, if any?
- What is the final cause and what is the relation of God with Newton’s theory.
- “He (God) governs everything, not as the soul of the world, but as the lord of all things.”
- “He is eternal and infinite, omnipotent and omniscient; that is, he endures from eternity to eternity, and is present from infinity to infinity. He reigns over everything, and knows everything that happens or can happen.”
- “God is one and the same God always and everywhere. He is omnipresent not in power alone, but also in substance. For power cannot subsist without substance. In him all things are contained and moved, but without mutual effects. God is not affected by the motions of bodies, and these do not experience any resistance from God’s omnipresence. It is universally acknowledged that the highest God exists necessarily, and by the same necessity he is always and everywhere.”
- “Hitherto I have set forth the phenomena of the heavens and of our sea through the force of gravity, but I have not yet assigned the cause of gravity.”
Remember: The Law of Universal Gravitation is not just that all particles with mass gravitate towards each other, but that they do so proportionately to the mass of each body and inversely as the square of the distances between the bodies.